Bilateral Subdiaphragmatic Vagal Nerve Stimulation Using a Novel Waveform Decreases Body Weight, Food Consumption, Adiposity, and Activity in Obesity-Prone Rats.

INTRODUCTION: Obesity affects millions of Americans. The vagal nerves convey the degree of stomach fullness to the brain via afferent visceral fibers. Studies have found that vagal nerve stimulation (VNS) promotes reduced food intake, causes weight loss, and reduces cravings and appetite. METHODS: Here, we evaluate the efficacy of a novel stimulus waveform applied bilaterally to the subdiaphragmatic vagal nerve stimulation (sVNS) for almost 13 weeks. A stimulating cuff electrode was implanted in obesity-prone Sprague Dawley rats maintained on a high-fat diet. Body weight, food consumption, and daily movement were tracked over time and compared against three control groups: sham rats on a high-fat diet that were implanted with non-operational cuffs, rats on a high-fat diet that were not implanted, and rats on a standard diet that were not implanted. RESULTS: Results showed that rats on a high-fat diet that received sVNS attained a similar weight to rats on a standard diet due primarily to a reduction in daily caloric intake. Rats on a high-fat diet that received sVNS had significantly less body fat than other high-fat controls. Rats receiving sVNS also began moving a similar amount to rats on the standard diet. CONCLUSION: Results from this study suggest that bilateral subdiaphragmatic vagal nerve stimulation can alter the rate of growth of rats maintained on a high-fat diet through a reduction in daily caloric intake, returning their body weight to that which is similar to rats on a standard diet over approximately 13 weeks.

Artificial neural network-based rapid predictor of biological nerve fiber activation for DBS applications.

Objective.Computational models are powerful tools that can enable the optimization of deep brain stimulation (DBS). To enhance the clinical practicality of these models, their computational expense and required technical expertise must be minimized. An important aspect of DBS models is the prediction of neural activation in response to electrical stimulation. Existing rapid predictors of activation simplify implementation and reduce prediction runtime, but at the expense of accuracy. We sought to address this issue by leveraging the speed and generalization abilities of artificial neural networks (ANNs) to create a novel predictor of neural fiber activation in response to DBS.Approach.We developed six variations of an ANN-based predictor to predict the response of individual, myelinated axons to extracellular electrical stimulation. ANNs were trained using datasets generated from a finite-element model of an implanted DBS system together with multi-compartment cable models of axons. We evaluated the ANN-based predictors using three white matter pathways derived from group-averaged connectome data within a patient-specific tissue conductivity field, comparing both predicted stimulus activation thresholds and pathway recruitment across a clinically relevant range of stimulus amplitudes and pulse widths.Main results.The top-performing ANN could predict the thresholds of axons with a mean absolute error (MAE) of 0.037 V, and pathway recruitment with an MAE of 0.079%, across all parameters. The ANNs reduced the time required to predict the thresholds of 288 axons by four to five orders of magnitude when compared to multi-compartment cable models.Significance.We demonstrated that ANNs can be fast, accurate, and robust predictors of neural activation in response to DBS.

A computational model of upper airway respiratory function with muscular coupling.

A two dimensional finite element model of upper airway respiratory function was developed emphasizing the effects of dilator muscular activation on the human retro-lingual airway. The model utilized an upright mid-sagittal computed tomography of the human head and neck to reconstruct relevant structures of the tongue, mandible, and the hyoid-related soft tissues, along with the retro-lingual airway. The reconstructed geometry was divided into fluid and solid domains and discretized into finite element (FE) meshes used for the computational model. Three cases were investigated: standing position; supine position; and supine position coupled with dilator muscle activation. Computations were performed for the inspiration stage of the breathing cycle, utilizing a fluid-structure interaction (FSI) method to couple structural deformation with airflow dynamics. The spatio-temporal deformation of the structures surrounding the airway wall were predicted to be in general agreement with known changes from upright to supine posture on luminal opening, as well as the distribution of airflow. The model effectively captured the effects of muscular stimulation on the upper airway anatomical changes, the flow characteristics relevant to airway reduction in the supine position and airway enlargement with muscle activation. The smallest airway opening in the retro-lingual section is predicted to occur at the epiglottic region in all the three cases considered, an unexpected vulnerable location of airway obstruction. The model also predicted that hyoid displacement would be associated with recovery from airway collapse. This information may be useful for building more complex models relevant to mechanisms and clinical interventions for obstructive sleep apnea.

Both high fat and high carbohydrate diets impair vagus nerve signaling of satiety.

Obesity remains prevalent in the US. One potential treatment is vagus nerve stimulation (VNS), which activates the sensory afferents innervating the stomach that convey stomach volume and establish satiety. However, current VNS approaches and stimulus optimization could benefit from additional understanding of the underlying neural response to stomach distension. In this study, obesity-prone Sprague Dawley rats consumed a standard, high-carbohydrate, or high-fat diet for several months, leading to diet-induced obesity in the latter two groups. Under anesthesia, the neural activity in the vagus nerve was recorded with a penetrating microelectrode array while the stomach was distended with an implanted balloon. Vagal tone during distension was compared to baseline tone prior to distension. Responses were strongly correlated with stomach distension, but the sensitivity to distension was significantly lower in animals that had been fed the nonstandard diets. The results indicate that both high fat and high carbohydrate diets impair vagus activity.

Quantification of clinically applicable stimulation parameters for precision near-organ neuromodulation of human splenic nerves.

Neuromodulation is a new therapeutic pathway to treat inflammatory conditions by modulating the electrical signalling pattern of the autonomic connections to the spleen. However, targeting this sub-division of the nervous system presents specific challenges in translating nerve stimulation parameters. Firstly, autonomic nerves are typically embedded non-uniformly among visceral and connective tissues with complex interfacing requirements. Secondly, these nerves contain axons with populations of varying phenotypes leading to complexities for axon engagement and activation. Thirdly, clinical translational of methodologies attained using preclinical animal models are limited due to heterogeneity of the intra- and inter-species comparative anatomy and physiology. Here we demonstrate how this can be accomplished by the use of in silico modelling of target anatomy, and validation of these estimations through ex vivo human tissue electrophysiology studies. Neuroelectrical models are developed to address the challenges in translation of parameters, which provides strong input criteria for device design and dose selection prior to a first-in-human trial.

Hypoglossal nerve stimulation in a rabbit model of obstructive sleep apnea reduces apneas and improves oxygenation.

Based on a prior anesthetized model, we developed an unanesthetized model to evaluate the effects of hypoglossal nerve stimulation (HNS) during sleep. We prepared three rabbits with injections of hyaluronic acid in the base of tongue to produce upper airway obstruction followed by HNS implant. Two rabbits were saline controls, and one, a passive control. Measures were sleep, airflow, effort, oxygen saturation, and heart rate. HNS with electrodes around the right hypoglossal nerve were adjusted to a level without behaviorally disturbing the animal. During HNS stimulation in the tongue-base injected rabbits, obstructive apneas and hypopneas of intermediate (3 to 7 cycles of respiratory effort) or longer (≥8 cycles) duration were largely eliminated while less clinically relevant shorter events (<3) were unaffected, and oxygen saturation was improved. Control animals exhibited no intermediate or long events. In this model HNS can relieve induced sleep apnea, without disturbing the animal: however, despite being non-canine and of substantial size, the model has its challenges.NEW & NOTEWORTHY This report describes a rabbit model for testing the impact of hypoglossal nerve stimulation (HNS) on obstructive apneas. Obstructive sleep apnea (OSA) is induced by injecting hyaluronic acid (as a filler) into the base of the tongue. HNS reduced the length and rate of obstructions and improved oxygenation during sleep. Our efforts with this model advanced understanding of the complexities of this OSA preclinical model for neurostimulation reversal of sleep-disordered breathing.

Toward Standardization of Electrophysiology and Computational Tissue Strain in Rodent Intracortical Microelectrode Models.

Progress has been made in the field of neural interfacing using both mouse and rat models, yet standardization of these models' interchangeability has yet to be established. The mouse model allows for transgenic, optogenetic, and advanced imaging modalities which can be used to examine the biological impact and failure mechanisms associated with the neural implant itself. The ability to directly compare electrophysiological data between mouse and rat models is crucial for the development and assessment of neural interfaces. The most obvious difference in the two rodent models is size, which raises concern for the role of device-induced tissue strain. Strain exerted on brain tissue by implanted microelectrode arrays is hypothesized to affect long-term recording performance. Therefore, understanding any potential differences in tissue strain caused by differences in the implant to tissue size ratio is crucial for validating the interchangeability of rat and mouse models. Hence, this study is aimed at investigating the electrophysiological variances and predictive device-induced tissue strain. Rat and mouse electrophysiological recordings were collected from implanted animals for eight weeks. A finite element model was utilized to assess the tissue strain from implanted intracortical microelectrodes, taking into account the differences in the depth within the cortex, implantation depth, and electrode geometry between the two models. The rat model demonstrated a larger percentage of channels recording single unit activity and number of units recorded per channel at acute but not chronic time points, relative to the mouse model Additionally, the finite element models also revealed no predictive differences in tissue strain between the two rodent models. Collectively our results show that these two models are comparable after taking into consideration some recommendations to maintain uniform conditions for future studies where direct comparisons of electrophysiological and tissue strain data between the two animal models will be required.

Selective stimulation of human intrinsic laryngeal muscles: Analysis in a mathematical three-dimensional space.

OBJECTIVES/HYPOTHESIS: Standard stimulating methods using square waves do not appropriately restore physiological control of individual intrinsic laryngeal muscles (ILMs). To further explore our earlier study of evoked orderly recruitment by quasitrapezoidal (QT) currents, we integrated the contribution of the cricothyroideus (CT) with attention to mutual activation in an additional patient, based on recent studies of appropriate responses via strict recurrent laryngeal nerve (RLN) stimulation. STUDY DESIGN: Basic science study. METHODS: The patient received functional electrical stimulation (FES) with QT pulses at 5 Hz, 60 to 2,000 µAmp, 100 to 500 µs pulse width, 0 to 500 µs decay. Ipsilateral electromyography (EMG) responses were calculated using the average maximum amplitude, area under the curve, and the root mean square of the rectified amplitude waveforms. The thyroarytenoideus (TA), posterior cricoarytenoideus (PCA), lateral cricothyroideus (LCA), and the CT were each interrogated via two monopolar electrodes, values were recorded in MATLAB, exported to Excel, and analyzed. Individual and mutual recruitment configurations and activation delays with stimulation were explored using multiple regression and exploration factor analyses. RESULTS: A total of 868 EMG data points based on 18 trials and up to 11 subtrials were captured from each of the four ILMs. Various combinations of pulse amplitude, pulse width, and exponential decay were found to produce significant (P ≤ .001) individual ILM responses. CT mirrored the LCA, whereas the TA and PCA exhibited separate interactions along shared trajectories in a three-dimensional space. CONCLUSIONS: FES calibrated to individual and coupled ILMs offers promise for restoring normal and pathological contraction patterns via strict RLN stimulation. LEVEL OF EVIDENCE: 5 Laryngoscope, 130:967-973, 2020.

Temporal Modulation of the Response of Sensory Fibers to Paired-Pulse Stimulation.

Multi-channel nerve cuff electrode arrays can provide sensory feedback to prosthesis users. To develop efficacious stimulation protocols, an understanding of the impact that spatio-temporal patterned stimulation can have on the response of sensory fibers is crucial. We used experimental and modelling methods to investigate the response of nerve fibers to paired-pulse stimulation. Nerve cuff electrode arrays were implanted for stimulation of the sciatic nerves of rats and the sensory compound action potentials were recorded from the L4 dorsal root. A model of the nerve cuff electrode array and sciatic nerve was also developed. The experimental and modelling results were compared. Experiments showed that it took 8 ms for the sensory fibers to completely recover from a conditioning stimulus, regardless of the relative position of the electrodes used for stimulation. The results demonstrate that the electrodes on the cuff cannot be considered independent. Additionally, at 120% of the threshold, there is a large overlap in the fibers that were activated by the different electrodes. If a stimulus paradigm considered the electrodes as independent, stimuli from the different electrodes would need to be interleaved, and the intervals between the stimuli should be greater than 8 ms.

Artificial tactile and proprioceptive feedback improves performance and confidence on object identification tasks.

Somatosensory feedback of the hand is essential for object identification. Without somatosensory feedback, individuals cannot reliably determine the size or compliance of an object. Electrical nerve stimulation can restore localized tactile and proprioceptive feedback with intensity discrimination capability similar to natural sensation. We hypothesized that adding artificial somatosensation improves object recognition accuracy when using a prosthesis. To test this hypothesis, we provided different forms of sensory feedback-tactile, proprioceptive, or both-to two subjects with upper limb loss. The subjects were asked to identify the size or mechanical compliance of different foam blocks placed in the prosthetic hand while visually and audibly blinded. During trials, we did not inform the subjects of their performance, but did ask them about their confidence in correctly identifying objects. Finally, we recorded applied pressures during object interaction. Subjects were free to use any strategy they chose to examine the objects. Object identification was most accurate with both tactile and proprioceptive feedback. The relative importance of each type of feedback, however, depended on object characteristics and task. Sensory feedback increased subject confidence and was directly correlated with accuracy. Subjects applied less pressure to the objects when they had tactile pressure feedback. Artificial somatosensory feedback improves object recognition and the relative importance of tactile versus proprioceptive feedback depends on the test set. We believe this test battery provides an effective means to assess the impact of sensory restoration and the relative contribution of different forms of feedback (tactile vs. kinesthetic) within the neurorehabilitation field.

Home Use of a Neural-connected Sensory Prosthesis Provides the Functional and Psychosocial Experience of Having a Hand Again.

The loss of a hand has many psychosocial repercussions. While advanced multi-articulated prostheses can improve function, without sensation, they cannot restore the full experience and connection of a hand. Direct nerve interfaces can restore naturalistic sensation to amputees. Our sensory restoration system produced tactile and proprioceptive sensations on the hand via neural stimulation through chronically implanted electrodes. In this study, upper limb amputees used a sensory-enabled prosthesis in their homes and communities, autonomously and unconstrained to specific tasks. These real-life conditions enabled us to study the impact of sensation on prosthetic usage, functional performance, and psychosocial experience. We found that sensory feedback fundamentally altered the way participants used their prosthesis, transforming it from a sporadically-used tool into a readily and frequently-used hand. Functional performance with sensation improved following extended daily use. Restored sensation improved a wide range of psychosocial factors, including self-efficacy, prosthetic embodiment, self-image, social interaction, and quality of life. This study demonstrates that daily use of a sensory-enabled prosthesis restores the holistic experience of having a hand and more fully reconnects amputees with the world.

Sciatic nerve stimulation and its effects on upper airway resistance in the anesthetized rabbit model relevant to sleep apnea.

Obstructive sleep apnea (OSA) is a disorder characterized by collapse of the velopharynx and/or oropharynx during sleep when drive to the upper airway is reduced. Here, we explore an indirect approach for activation of upper airway muscles that might affect airway dynamics, namely, unilateral electrical stimulation of the afferent fibers of the sciatic nerve, in an anesthetized rabbit model. A nerve cuff electrode was placed around the sciatic and hypoglossal nerves to deliver stimulus while airflow, air pressure, and alae nasi electromyogram (EMG) were monitored both before and after sciatic transection. Sciatic nerve stimulation increased respiratory effort, rate, and alae nasi EMG, which persisted for seconds after stimulation; however, upper airway resistance was unchanged. Hypoglossal stimulation reduced resistance without altering drive. Although sciatic nerve stimulation is not ideal for treating OSA, it remains a target for altering respiratory drive. NEW & NOTEWORTHY Previously, sciatic nerve stimulation has been shown to activate upper airway and chest wall muscles. The supposition that resistance through the upper airway would be reduced with this afferent reflex was disproven. Findings were in contrast with the effect of hypoglossal nerve stimulation, which was shown to decrease resistance without changing muscle activation or ventilatory drive.

Sensory adaptation to electrical stimulation of the somatosensory nerves.

OBJECTIVE: Sensory systems adapt their sensitivity to ambient stimulation levels to improve their responsiveness to changes in stimulation. The sense of touch is also subject to adaptation, as evidenced by the desensitization produced by prolonged vibratory stimulation of the skin. Electrical stimulation of nerves elicits tactile sensations that can convey feedback for bionic limbs. In this study, we investigate whether artificial touch is also subject to adaptation, despite the fact that the peripheral mechanotransducers are bypassed. APPROACH: Using well-established psychophysical paradigms, we characterize the time course and magnitude of sensory adaptation caused by extended electrical stimulation of the residual somatosensory nerves in three human amputees implanted with cuff electrodes. MAIN RESULTS: We find that electrical stimulation of the nerve also induces perceptual adaptation that recovers after cessation of the stimulus. The time course and magnitude of electrically-induced adaptation are equivalent to their mechanically-induced counterparts. SIGNIFICANCE: We conclude that, in natural touch, the process of mechanotransduction is not required for adaptation, and artificial touch naturally experiences adaptation-induced adjustments of the dynamic range of sensations. Further, as it does for native hands, adaptation confers to bionic hands enhanced sensitivity to changes in stimulation and thus a more natural sensory experience.

Hypoglossal nerve stimulation in a pre-clinical anesthetized rabbit model relevant to OSA.

We tested the functional effects of hypoglossal (CNXII) stimulation in the anesthetized rabbit before and after injections of saline into the tongue base to obstruct the airway. Data (n = 6) show little or no effect of CN XII trunk stimulation; however, medial branch stimulation (20-100 Hz; 50-500 µs pulse width, and incremental increases from 10 µA) reduced upper airway resistance. Medial branch stimulation was less effective in reducing resistance than anterior advancement of the hyoid. Endoscopic viewing (n-3) of the retropalate showed this region as the narrowest and dynamically changed by anterior hyoid displacement, with less evident effects than CNXII stimulation. We conclude that under these conditions CNXII medial branch stimulation reduces airway resistance, especially after induced obstruction.

The neural basis of perceived intensity in natural and artificial touch.

Electrical stimulation of sensory nerves is a powerful tool for studying neural coding because it can activate neural populations in ways that natural stimulation cannot. Electrical stimulation of the nerve has also been used to restore sensation to patients who have suffered the loss of a limb. We have used long-term implanted electrical interfaces to elucidate the neural basis of perceived intensity in the sense of touch. To this end, we assessed the sensory correlates of neural firing rate and neuronal population recruitment independently by varying two parameters of nerve stimulation: pulse frequency and pulse width. Specifically, two amputees, chronically implanted with peripheral nerve electrodes, performed each of three psychophysical tasks-intensity discrimination, magnitude scaling, and intensity matching-in response to electrical stimulation of their somatosensory nerves. We found that stimulation pulse width and pulse frequency had systematic, cooperative effects on perceived tactile intensity and that the artificial tactile sensations could be reliably matched to skin indentations on the intact limb. We identified a quantity we termed the activation charge rate (ACR), derived from stimulation parameters, that predicted the magnitude of artificial tactile percepts across all testing conditions. On the basis of principles of nerve fiber recruitment, the ACR represents the total population spike count in the activated neural population. Our findings support the hypothesis that population spike count drives the magnitude of tactile percepts and indicate that sensory magnitude can be manipulated systematically by varying a single stimulation quantity.

Sensory feedback by peripheral nerve stimulation improves task performance in individuals with upper limb loss using a myoelectric prosthesis.

OBJECTIVE: Tactile feedback is critical to grip and object manipulation. Its absence results in reliance on visual and auditory cues. Our objective was to assess the effect of sensory feedback on task performance in individuals with limb loss. APPROACH: Stimulation of the peripheral nerves using implanted cuff electrodes provided two subjects with sensory feedback with intensity proportional to forces on the thumb, index, and middle fingers of their prosthetic hand during object manipulation. Both subjects perceived the sensation on their phantom hand at locations corresponding to the locations of the forces on the prosthetic hand. A bend sensor measured prosthetic hand span. Hand span modulated the intensity of sensory feedback perceived on the thenar eminence for subject 1 and the middle finger for subject 2. We performed three functional tests with the blindfolded subjects. First, the subject tried to determine whether or not a wooden block had been placed in his prosthetic hand. Second, the subject had to locate and remove magnetic blocks from a metal table. Third, the subject performed the Southampton Hand Assessment Procedure (SHAP). We also measured the subject's sense of embodiment with a survey and his self-confidence. MAIN RESULTS: Blindfolded performance with sensory feedback was similar to sighted performance in the wooden block and magnetic block tasks. Performance on the SHAP, a measure of hand mechanical function and control, was similar with and without sensory feedback. An embodiment survey showed an improved sense of integration of the prosthesis in self body image with sensory feedback. SIGNIFICANCE: Sensory feedback by peripheral nerve stimulation improved object discrimination and manipulation, embodiment, and confidence. With both forms of feedback, the blindfolded subjects tended toward results obtained with visual feedback.

Stability and selectivity of a chronic, multi-contact cuff electrode for sensory stimulation in human amputees.

OBJECTIVE: Stability and selectivity are important when restoring long-term, functional sensory feedback in individuals with limb-loss. Our objective is to demonstrate a chronic, clinical neural stimulation system for providing selective sensory response in two upper-limb amputees. APPROACH: Multi-contact cuff electrodes were implanted in the median, ulnar, and radial nerves of the upper-limb. MAIN RESULTS: Nerve stimulation produced a selective sensory response on 19 of 20 contacts and 16 of 16 contacts in subjects 1 and 2, respectively. Stimulation elicited multiple, distinct percept areas on the phantom and residual limb. Consistent threshold, impedance, and percept areas have demonstrated that the neural interface is stable for the duration of this on-going, chronic study. SIGNIFICANCE: We have achieved selective nerve response from multi-contact cuff electrodes by demonstrating characteristic percept areas and thresholds for each contact. Selective sensory response remains consistent in two upper-limb amputees for 1 and 2 years, the longest multi-contact sensory feedback system to date. Our approach demonstrates selectivity and stability can be achieved through an extraneural interface, which can provide sensory feedback to amputees.

A neural interface provides long-term stable natural touch perception.

Touch perception on the fingers and hand is essential for fine motor control, contributes to our sense of self, allows for effective communication, and aids in our fundamental perception of the world. Despite increasingly sophisticated mechatronics, prosthetic devices still do not directly convey sensation back to their wearers. We show that implanted peripheral nerve interfaces in two human subjects with upper limb amputation provided stable, natural touch sensation in their hands for more than 1 year. Electrical stimulation using implanted peripheral nerve cuff electrodes that did not penetrate the nerve produced touch perceptions at many locations on the phantom hand with repeatable, stable responses in the two subjects for 16 and 24 months. Patterned stimulation intensity produced a sensation that the subjects described as natural and without "tingling," or paresthesia. Different patterns produced different types of sensory perception at the same location on the phantom hand. The two subjects reported tactile perceptions they described as natural tapping, constant pressure, light moving touch, and vibration. Changing average stimulation intensity controlled the size of the percept area; changing stimulation frequency controlled sensation strength. Artificial touch sensation improved the subjects' ability to control grasping strength of the prosthesis and enabled them to better manipulate delicate objects. Thus, electrical stimulation through peripheral nerve electrodes produced long-term sensory restoration after limb loss.

Probabilistic modeling of selective stimulation of the human sciatic nerve with a flat interface nerve electrode.

Ankle control is critical to both standing balance and efficient walking. The hypothesis presented in this paper is that a Flat Interface Nerve Electrode (FINE) placed around the sciatic nerve with a fixed number of contacts at predetermined locations and without a priori knowledge of the nerve's underlying neuroanatomy can selectively control each ankle motion. Models of the human sciatic nerve surrounded by a FINE of varying size were created and used to calculate the probability of selective activation of axons within any arbitrarily designated, contiguous group of fascicles. Simulations support the hypothesis and suggest that currently available implantable technology cannot selectively recruit each target plantar flexor individually but can restore plantar flexion or dorsiflexion from a site on the sciatic nerve without spillover to antagonists. Successful activation of individual ankle muscles in 90% of the population can be achieved by utilizing bipolar stimulation and/or by using a cuff with at least 20 contacts.

Probabilistic modeling of selective stimulation of the human sciatic nerve with a flat Interface Nerve Electrode.

Proper ankle control is critical to both standing balance and efficient walking. This study hypothesized that a Flat Interface Nerve Electrode (FINE) placed around the sciatic nerve with a fixed number of contacts at predetermined locations and without a priori knowledge of the nerve's underlying neuroanatomy can selectively control each ankle motion. Models of the human sciatic nerve surrounded by a FINE of varying size were created and used to calculate the probability of selective activation of axons within any arbitrarily designated group of fascicles. Simulations suggest that currently available implantable technology cannot selectively recruit each target plantar flexor individually but can restore plantar flexion or dorsiflexion from a site on the sciatic nerve without spillover to antagonists. Successful activation of individual ankle muscles in 90% of the population can be achieved by utilizing bipolar stimulation and/or by increasing the number of contacts within the cuff.